All the variable speed graphical post processing start with *plot_VS*, they can be accessed with by using the Matlab auto-completion or in the post_processing documentation

The variable speed SPL can be displayed with plot_VS_ASPL_overall

The green line corresponds to the speed above which field weakening is applied. The red line corresponds to the speed above which the spectrum is complete up to specified maximum frequency Input.Simu.freq_max_spec.
One can see that when running the machine at variable speed, two resonances occur close to 380 and 1170 rpm.

It corresponds to two slotting lines of wavenumber r=2 exciting the ovalization mode the stator stack that were identified in the theoretical analysis.

A slight resonance occurs at 1440 rpm too. To further understand where this resonance come from, one can plot the sonogram (variable speed noise spectrum) with plot_VS_ASPL_sonagram

If you are not familiar with this graph you can refer to our detailed article on what is a spectrogram?.

The empty / white part of the graph below 700 rpm corresponds to missing high frequency content. This is a consequence of the Load Extrapolation Algorithm based on a single speed calculation: if the single speed frequency resolution is not small enough, the largest frequency at low speed can drop below the specified maximum frequency.

To avoid that one should preferably start form the operating point of the lowest speed, by reducing the speed to **Input.Simu.N0 = (300/1200)*60*60/3**
and the voltage to **Input.Simu.U0 = (300/1200)*300/sqrt(3)**
In that case the new overall SPL and sonogram are given by (plot_VS_ASPL_overall; plot_VS_ASPL_sonagram) :

One can see that the spectra are full, and that the overall noise level is actually unchanged: the completion of the spectra has not introduced new high frequency magnetic forces. This is generally the case as all exciting forces are proportional to the speed, so the warning linked to the load extrapolation algorithm can be ignored.

The natural frequencies calculated by MANATEE are also displayed in the sonograms as vertical dashed lines in the graph. One can see that two magnetic excitations enters in resonance with the (2,0) mode close to 270 and 1170 rpm, and that the third resonance close to 1440 rpm is due to the fourth order elliptical mode of the stack. By checking the theoretical analysis, **this wavenumber 4 was also identified theoretically as linked to kr=4 and ks=3**.

The contribution of this fourth wavenumber can also be checked with the variable speed modal contribution to acoustic noise level (plot_VS_ASWL_modal_cont) :

To check our interpretations one can additionally make a “tracking order” analysis which consists in tracking some specific acoustic lines of the sonogram defined by their slope during a linear run-up (the slope is called a mechanical “order” but has nothing to do with a spatial wavenumber of a force wave). MANATEE can automatically track the most relevant acoustic lines due to magnetic noise based on the theoretical identification previously detailed with plot_VS_ASWL_order_analysis

One can find again the two excitation of wavenumber 2 and 4 creating three successive resonances.